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Recent observations of binary black hole and binary neutron star mergers have ignited interest in the formation and evolution of compact-object binaries. One of the most pressing questions is determining the formation environments of these systems which couple strongly to their population characteristics. However, by the time a compact-object binary merges and produces the gravitational-wave signals observed by ground-based detectors, much of the evolutionary history of the system is washed away. By combining binary population synthesis simulations with gravitational-wave and electromagnetic observations, we can constrain uncertain processes that govern the evolution of binary stars from their birth through to compact object formation and merger. In this talk I will highlight recent work which explores ways to combine binary population simulations with current and future data from gravitational-wave and electromagnetic surveys to constrain the formation and evolution of binary stars and compact object binaries.